A combined method for computing the field of the point source in a waveguide (plane-layered media). (Russian, English) Zbl 1130.35122

J. Math. Sci., New York 132, No. 1, 113-129 (2006); translation from Zap. Nauchn. Semin. POMI 308, 197-224, 255-256 (2004).
Summary: The two-dimensional problem of propagating the waves generated by a point source, in a depth plane-layered waveguide is investigated. The Dirichlet condition is given on the boundary of the waveguide and also two consistency conditions are defined on the interface between the fluid and the bottom. The velocity of acoustic waves is assumed to be dependent only on the depth of the waveguide. With the help of cumbersome transformations, the solution is represented as a sum of geometric-optical waves, normal waves, and a remainder. Sufficient conditions on the total amount of detached normal and geometric-optical waves are obtained. The remainder is expressed by a simple formula.


35Q60 PDEs in connection with optics and electromagnetic theory
76Q05 Hydro- and aero-acoustics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A05 Geometric optics
78A50 Antennas, waveguides in optics and electromagnetic theory
Full Text: DOI EuDML


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